This proposed project is a non-conventional framework for RNA 3D structure prediction from sequences. It solves the 3D structure prediction problem with a novel graph-theoretic model of backbone k-tree that has the potential to markedly reduce the molecular 3D conformation space. Specific objectives of this research are: (1) to develop the proposed structure prediction framework into deliverable tools with the desired accuracy and the ability to scale to large RNA molecules; (2) to establish algorithmic graph theory for backbone k-tree optimization serving as the foundation for the prediction algorithm development; and (3) to validate and improve the prediction method by incorporating structural studies and biochemical experiments with selected model non-coding RNAs. Computational prediction of RNA 3D structure is critical for understanding cellular functions of non-coding RNAs. However, identifying native structures from RNA sequences has proven to be a significant challenge due to the difficulty of searching the immense space of 3D conformations even for a small RNA molecule. Prediction accuracy can be compromised by non-optimal, sampling techniques often adopted for computational feasibility; in particular, existing methods have yet to deliver the desired performance for RNA sequences of more than 50 nucleotides. This project proposes to directly address this challenging issue with a novel backbone k-tree model for nucleotide interaction relationships that specify the 3D conformation. The model significantly reduces the search space of conformations and potentially enables efficient algorithms for 3D structure prediction. To bring this capability to fruition, this research will undertake a full investigation of the unexplored algorithmic graph theory of backbone k-trees. A thorough understanding of such a theory will not only benefit the RNA 3D structure prediction but also offer viable solutions to other challenging problems such as RNA-RNA complex prediction. Accurate and scalable tools for 3D structure prediction will permit effective structure elucidation of newly discovered RNAs.